[Paper Review] The complementarity of astrometric and radial velocity exoplanet observations - Determining exoplanet mass with astrometric snapshots

Mikko Tuomi, S. Kotiranta+1 more|ArXiv.org|Jul 15, 2008

Stellar, planetary, and galactic studies27 references9 citations

TL;DR

This paper demonstrates that combining radial velocity (RV) and astrometric measurements via Bayesian inference enables detection of exoplanet masses with observational timelines significantly shorter than the orbital period. Using simulated data, it shows that a Jupiter analog at 30 pc can be detected with 3 years of astrometry (vs. 12-year orbital period), and HD 154345b's true mass can be determined in just one year of astrometry when combined with 20 years of RV data.

ABSTRACT

We obtain full information on the orbital parameters by combining radial velocity and astrometric measurements by means of Bayesian inference. We sample the parameter probability densities of orbital model parameters with a Markov chain Monte Carlo (McMC) method in simulated observational scenarios to test the detectability of planets with orbital periods longer than the observational timelines. We show that, when fitting model parameters simultaneously to measurements from both sources, it is possible to extract much more information from the measurements than when using either source alone. We demonstrate this by studying the orbit of recently found extra-solar planet HD 154345 b.

Motivation & Objective

• To test the assumption that exoplanet detection via astrometry or radial velocity requires observational timelines longer than the orbital period.
• To determine the minimum observational timeline required for positive detection of exoplanets using combined high-precision RV and astrometric data.
• To demonstrate that Bayesian inference on multi-source data can extract full orbital parameters, including true mass and inclination, even with short timelines.
• To evaluate the feasibility of determining the true mass of known RV planets like HD 154345b using future astrometric missions such as SIM.

Proposed method

• Uses Bayesian inference to combine radial velocity and astrometric measurements into a unified model for exoplanet parameter estimation.
• Applies Markov Chain Monte Carlo (MCMC) sampling to explore the full posterior probability density of orbital and reference frame parameters.
• Simulates astrometric measurements with 1 µas precision (SIM-like) and RV measurements with 1 m/s precision to model realistic observational scenarios.
• Models the star’s motion as a two-body system using Keplerian orbital elements and Cartesian coordinates, with parameters including semi-major axis, eccentricity, inclination, and longitude of pericentre.
• Generates synthetic astrometric data for varying observation durations (T_A = 0.8 to 10 years) to test detectability of orbital plane parameters (I, Ω).
• Compares results from RV-only analysis (Wright et al. 2008) with joint RV-astrometry inference to quantify improvements in parameter uncertainty and detection power.

Experimental results

Research questions

• RQ1 Can exoplanets with orbital periods longer than the observational timeline be detected using combined astrometric and radial velocity data?
• RQ2 What is the minimum observational timeline required for astrometric measurements to determine the true mass of a planetary companion?
• RQ3 How does combining RV and astrometric data improve the precision of orbital parameter estimation compared to using either method alone?
• RQ4 To what extent can Bayesian inference with MCMC sampling resolve the inclination and true mass of a planet when the timeline is shorter than the orbital period?
• RQ5 Can the true mass of HD 154345b be determined with a single year of astrometric observations if 20 years of RV data are already available?

Key findings

• A Jupiter analog at 30 pc can be detected and its true mass determined with only 3 years of astrometric observations, despite its 12-year orbital period.
• With 20 years of radial velocity data, astrometric observations of just one year are sufficient to determine the true mass of HD 154345b using the SIM telescope.
• For HD 154345b, the 99% Bayesian confidence intervals for inclination (I) and longitude of ascending node (Ω) were [-0.30, 0.22] and [0.39, 1.54] radians, respectively, with only one year of astrometry.
• Joint Bayesian inference of RV and astrometric data reduces parameter uncertainties more effectively than RV-only analysis, with tighter confidence intervals than the Bootstrap method used in prior work.
• The method successfully recovers orbital parameters consistent with prior studies but with improved precision due to direct posterior sampling.
• The study confirms that the commonly held assumption requiring observation timelines longer than the orbital period is not necessary when multiple data sources are combined via Bayesian inference.